In a study of college student performance conducted in 2017.

In a study of college student performance conducted in 2017, it was found that students from School A have a mean GPA of 3.1. Assume that the GPAs were normally distributed. Question 1: Find the mean of the sampling distribution of the mean GPA (X) for samples of size 81. Question 2: Suppose that the standard deviation of the sampling distribution of the mean GPA for samples of size 25 is 0.09. Find the standard deviation of the sampling distribution of the mean GPA for samples of size 81. Question 3: Under the assumption of Question 2, find the probability that a random sample of 9 students will have a mean GPA greater than 3.25. Question 4: Suppose that among the students who earned a GPA of 3.5 or above, 52% were females. For a random sample of 400 students who earned a GPA of 3.5 or above, find the probability that more than 55% of them are males. In another study conducted in the same year (2017), it was found that students from School B have a mean GPA of 2.8. Consider a random sample of 81 students from School A (sample 1) and a random sample of 25 students from School B (sample 2). Denote the mean GPA of the two samples by X, and X2 Question 5: Find the mean of the sampling distribution of X1 - X2- Question 6: Suppose that the standard deviation of the sampling distribution of the mean GPA for samples of size 25 from School A is 0.09, and that the standard deviation of the sampling distribution of the mean GPA for samples of size 81 from School B is 0.1. Find the standard deviation of the sampling distribution of X1 - X2- Question 7: Under the assumption of Questions 5 and 6, find the probability that X, - X2